Generating Whole Numbers – the Power of 5 Twos

It seems to me now that mathematics is capable of an artistic excellence as great as that of any music, perhaps greater; not because the pleasure it gives (although very pure) is comparable, either in intensity or in the number of people who feel it, to that of music, but because it gives in absolute perfection that combination, characteristic of great art, of godlike freedom, with the sense of inevitable destiny; because, in fact, it constructs an ideal world where everything is perfect and yet true.

Bertrand Russell

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Whole numbers are the part of the number system. It includes all the natural numbers and zero (0). In set theoretic notation, we can write it as W = {0, 1, 2, 3, . . .}.

On other hand, among many mathematical operations, addition (+), subtraction (−), multiplication (×), division (÷), fraction (a/b), reciprocal (1/x), exponentiation (ax), square root (√), concatenation (xx), factorial (!), decimal (.) etc. are well known.

There is a famous mathematics problem in which we are allowed to use 5 twos and any mathematical operations to generate various whole numbers. In this article, we will show the way to generate whole numbers up to 26 using 5 twos. But we can generate other numbers also. Here, we have considered a few ways to represent a particular number, so the list is not exhaustive. If you came across any other way(s) to represent a number, not listed here, please do get back to us.

First we will generate the whole numbers 0, 1 and 2 using 5 twos. The list is given below.

Next we will generate the whole numbers 3, 4, 5 and 6 using 5 twos. The list is given below.

Then the turn for generating the whole numbers 7, 8, 9 and 10 using 5 twos. The list is given below.

We can generate the whole numbers 11, 12, 13 and 14 using 5 twos as below.

Now we will generate the whole numbers 15, 16 and 17 using 5 twos. The list is given below.

We can generate the whole numbers 18, 19 and 20 using 5 twos as given below.

Now the turn for generating the whole numbers 21, 22 and 23 using 5 twos. The list is given below.

Finally, we will generate the whole numbers 24, 25 and 26 using 5 twos. The list is given below.

Your suggestions are eagerly and respectfully welcome! See you soon with a new mathematics blog that you and I call Math1089 – Mathematics for All!“.